Mehtod and apparatus for quantifying tissue histology

ABSTRACT

Method of analysing at least one parameter of a body component is provided. The method includes illuminating the component or body with light of at least a first and second waveband, receiving light of at least said first and second wavebands remitted by the component at a photoreceptor or photoreceptors, and analysing the light received at the photoreceptor(s) to provide a ratio between the amount of light remitted at the first waveband and the amount of light remitted of the second waveband, and from this calculating the component parameter.

This invention relates to a method and apparatus for quantifying tissuehistology. In particular the invention relates to methods using ananalysis of the spectra of remitted light to establish information onthe properties of the tissue. The invention is also applicable tomethods and apparatus which rely upon a spectral analysis of lightremitted, emitted, andor transmitted from any material or object undertest where they have parameters exhibiting wavelength specific opticaleffects.

There exists the need for a system, which can recover histologicalparameters from biological tissue in a way which is invariant to theintensity of the incident illumination and scene geometry. It is anobjective of the present invention to provide such a technique. Such asystem would be of value in systems where the topology of the tissue orimage surface in not known a priori. It would also be of value in asystem where the intensity of the illuminating light cannot be assumedconstant. Potential applications include but are not limited to imagingand analysis of the tissue of the gastrointestinal track with anendoscope and imaging and analysis of skin over areas where there is asignificant change in curvature, such as the face.

A system is currently in existence, which is able to assist cliniciansin their diagnosis of melanoma. The technique is based on a patent,international patent application publication number W098/22023. Thissystem is based on the discovery that when the range of colouration ofnormal human skin is plotted in a standard RGB colour space, it lies ona well-defined surface. Furthermore, if an abnormality such as dermalmelanin is present, the colouration of the skin changes in such a way asto move points away from the surface which describes healthy skin. Byincorporating a calibration calculation which allows variation of dermalthickness to be taken into account, the technique is able to detectabnormalities and thus assist clinicians in their diagnosis of melanoma

The fundamental principle behind this system is that it is possible toconstruct a mathematical function that relates image values, measuredusing a digital camera, to appropriate histological parameters. Usingthis functional relation, it is possible to obtain the value of eachparameter at every point across a given image. A parametric map can thenbe produced which gives a grey-scale representation of the parametervalue across the whole image.

Although this system has been proved to be clinically effective, itrequires exact calibration of the illuminating light source and does nottake into account any variation in surface geometry. Thus the techniqueis limited to problems where a probe can be placed in contact with theregion of interest. This ensures that the incident light is controlledand calibrated and that it's angle of incidence remains constant.

The proposed invention relates to a method for imaging tissue in such away to give quantitative spectral data independently of the surfacegeometry or the intensity of the illuminating light. This will allow anon-contact form of imaging and analysis which will be applicable tomany different applications. The method may be used with the techniquedescribed in W098/22023 and subsequent related patents but is notexclusive to it.

The method concentrates upon the analysis of light remitted by thetissue, in the illuminating light which penetrates the tissue to somedepth and is reflected (or scattered or/and absorbed) to differentdegrees at different depths due to different parameters of the tissue.Effects due to surface reflection are to be eliminated from theanalysis.

Substantial work has been carried out to develop image analysisalgorithms which are able to identify different objects irrespective ofthe illuminating light. Many of the techniques developed are basedaround the linear model of surface reflectance as proposed in L Maloneyand B. Wandell, “Color constancy: a method for recovering surfacespectral reflectance”, J. Opt. Soc. Am. A 3, 29-33 (1986). This approachis based on the idea that the surface reflectance of any object withinan imaged scene can be expressed as a weighted sum of basis spectralreflectance functions: $\begin{matrix}{{S(\lambda)} = {\sum\limits_{j = 1}^{n}{\sigma_{j}{S_{j}(\lambda)}}}} & (1)\end{matrix}$and that the illuminating light can similarly be expressed as a weightedsum of basis lights. It has been shown that only a small number of basisfunctions are required to obtain accurate approximations to the surfacereflectances of many naturally occurring objects and also the spectralvariation of natural daylight.

With this technique it is possible to recover the vector of weightingconstants σ_(j) from a vector of image values and thus specify thespectral reflectance of the imaged object at every pixel. Everypotential imaged object object characteristic will have a uniquespectral reflectance. Thus, if the spectral reflectance can bedetermined using a linear model, then the parameter vector can bespecified. With this approach it should be possible to recover aparameter vector from the vector of image values at each pixel.Unfortunately the method is only able to recover the weighting constantsσ_(j) to within a multiplicative scaling factor and thus cannot be usedto specify the exact spectral reflectance and therefore the exactparameter vector.

An approach to geometry-insensitive segmentation of images has beendeveloped in G. Healey, “Using colour for geometry-insensitivesegmentation,” J. Opt. Soc. Am. A 6, 920-937 (1989), and is based on theidea of normalised colour. With this approach image values are firstdivided by an estimate of normalised colour. This estimate is based onapproximating the incoming signal from colour pixel values by using afinite-dimensional linear approximation to represent the colour signal.

Using these normalised values, different metal and dielectric materialscan be identified across an imaged scene in which the geometry variesconsiderably.

A similar technique has been applied to evaluate burn injuries {M. A.Afromowitz, G. S. van Liew and D. M. Heimbach, “Clinical evaluation ofburn injuries using an optical reflectance technique”, IEEE trans.Biomed. Eng. BME-34, 114-127 (1987), and M. A. Afromowitz, J. B. CallisD. M. Heimbach, L. A. Desoto and M. K. Norton, “Mulitspectral imaging ofburn wounds: a new clinical instrument for evaluating burn depth”, IEEEtran. Biomed. Eng. 35, 842-849 (1988)}. In this case, RGB image valueswere normalised by dividing them by the response of an IR filter. Fromthe normalised values it was possible to assess the extent of burndamage across a given area of imaged skin.

There exists a need for a non-invasive technique for analysing an objector material (which may be complex, for example multi-component and/ormulti-layer and which may be solid, gaseous, liquid, etc) which does notrequire calibration to take into account changing illuminationconditions.

SUMMARY OF THE INVENTIONS

According to a first aspect of the invention there is provided a methodof analyzing at least one parameter of a body component, comprising thesteps of illuminating the component with light of at least a first andsecond waveband, receiving light of at least said first and secondwavebands remitted by the component at a photoreceptor, and analyzingthe light received at the photoreceptor to provide a ratio between theamount of light remitted of the first waveband and the amount of lightremitted of the second waveband, and from this calculating the componentparameter.

Thus the invention lies in the appreciation that by skillful selectionof the wavebands of light remitted by a biological component, usuallyhuman or animal tissue, the ratio between two such wavebands can be usedto create a useful parametric image of the biological component. Thewavebands may be calculated using a biological or mathematical model tomonitor the relationship between a particular image ratio and theparameter to create a function which then can be used for monitoringthat parameter in the biological component. As an alternative tocreating a function the measured waveband ratios can be compared withthe predictions of a model either mathematical or experimentiallymeasured.

According to a second aspect of the invention, there is provided amethod of analyzing at least one parameter of a body component,comprising the steps of illuminating the component with light of atleast a first and second predetermined waveband, receiving light of atleast said first and second predetermined wavebands remitted by thecomponent reflected by the surface at a photoreceptor but eliminatinglight reflected by the surface of the component, where the predeterminedwavebands are chosen such that the component parameter is a one to onefunction of the ratio between the amount of light remitted by thecomponent of the first predetermined wavebands and the amount of lightremitted by the component of the second predetermined waveband, andanalyzing the light received at the photoreceptor to provide a ratiobetween the light of the first waveband and the light of the secondwaveband, and from this calculating the component parameter.

The method is such that the effects of reflection rather than remittancewill be ignored. Although this would appear to limit the application tocomponents which do not have a specular component of reflection, such asmany organic objects, image processing algorithms have been developed toallow removal of this component of reflection giving greaterapplicability of the technique. For example, it has been shown that itis possible to remove the highlights from complex images containinginhomogeneous dielectrics. It is also possible to remove the surfacecomponent of reflection using a polarising filter. Once this componenthas been removed from image data, it will be possible to use thetechniques described here.

Preferably the effects of surface reflection are eliminated by providinga pair of cross-polarised linear polarizing filters. The first of theseis placed in front of the source of illumination and the second in frontof the image capture system. There are however other methods which willbe apparent the skilled reader which could be used to eliminate surfacereflection effects.

The body component may be any biological component but is most usefullyanimal tissue.

Each waveband referred to may comprise a single wavelength, but inpractice will preferably comprise a band of wavelengths, detectable bythe photoreceptor.

The light emitted by the light source may be a white light or light of aplurality of wavelengths, some of which are outside the predeterminedwavebands, and filters may be used to limit the light received by thephotoreceptor to the desired wavebands. Such filters may be placedbetween the light source and the tissue, between the tissue and thephotoreceptor or at both positions. Alternatively white light may beemitted by the light source and received by the photoreceptor with theanalysis means establishing the amount of light within the desiredwaveband.

To understand why this process eliminates any variation in illuminationintensity and surface geometry it is necessary to consider thedichromatic reflection model. This was first proposed by S. Shafer in“Using colour to separate reflection components” Color. Res. Appl. 4,210-218 (1985) and states that light remitted from an object is the sumof two components, the “body” component and the “surface” component. Thebody component refers to physical processes occurring after penetrationof light into the material and the surface term to reflections whichtake place at the surface of the object. The body component is afunction of the spectral characteristics of the object, whereas thesurface component depends only on the object geometry and the incidentlight. The theory states further that each component can be consideredthe product of a geometrical term and a wavelength dependent term.

The proposed invention is used where an optical system makes spectralmeasures of tissue. One embodiment of such an optical system uses acolour digital camera as the photoreceptor, although a monochromedigital camera arranged to take sequential images with differentcoloured light sources could also be used. Both these embodiments mayhave millions of image pixels or very few pixels, or even just one pixelin the case of the monochrome system. The optical system may work in thevisual spectrum, or over an extended spectrum to include non visiblewavelengths. These non visible wavelengths may include infra-red light.This infra-red light may include wavelengths in the 600 nm to 800 nmband.

In the case of a conventional colour digital camera, the system measureslight through a number of optical filters. Image values for a specificimage location, corresponding to the nth filter, are given byi ^(n) =K _(b) C _(b) ^(n) +K _(s) C _(s) ^(n)where K_(b) and K_(s) are the geometric terms of the body and surfacecomponent respectively and C_(b) and C_(s) are colour terms. By usingthe system of polarising filters described above it is possible toeliminate surface reflection. Image values are then given as a simpleproduct of a geometric term and a colour, or wavelength dependent term.The illuminating light is now written asE(λ)=ε₀ E ₀(λ)where ε₀ is a wavelength independent scaling factor determined by theintensity of the light source but which does not change, or changes in aknown manner, will wavelength. This allows the dichromatic reflectionmodel to be written asi ^(n) =ε∫E ₀(λ)S(λ)R ^(n)(λ)dλwhere ε=ε₀K_(b). The function R^(n)(λ) defines the spectral response ofthe nth filter and S^(n)(λ) the remitted spectrum of the illuminatedtissue. It is essential that both E₀(λ) and R^(n)(λ) are known for thegiven imaging system. Thus the invention is preferentially utilised into systems where tissue of interest is illuminated with light of knowspectral characteristics.

If the optical system records a M-dimensional vector of image values ateach pixel then it is possible to define a N-dimensional vector of imageratios, which is obtained by defining appropriate ratios of imagevalues. An example of such a vector is$r = {\left\langle {\frac{i_{2}}{i_{1}},\frac{i_{3}}{i_{1}},\ldots\quad,\frac{i_{M}}{i_{1}}} \right\rangle.}$

As the constant ε depends only on position within an image allcomponents of the ratio vector r will be independent of the constant εand thus independent of the illumination intensity and geometricalfactors in the imaged scene.

The invention is applicable to problems in which all histologicalvariation can be described by K parameters. The concept of a parametervector is introduced and defined asp=(p ₁ , p ₂ , . . . , p _(K))p∈Pwhere the space P defines all possible parameter variation and thusvariation in tissue histology. Using the current invention it ispossible to recover a parameter vector from a vector of image ratios. Toachieve this it is necessary to have some technique for predicting avector of image ratios from a given parameter vector. This can beachieved via some experimental technique or with an appropriatemathematical model of light transport within the tissue of interest.Techniques such as Monte Carlo modelling or the Kubelka-Munkapproximation have been developed for this purpose. With such a model itis possible to predict a remittance spectrum which corresponds to aunique point in parameter space, that is a unique tissue histology. Witha knowledge of the spectral response of the illuminating light sourceand the spectral response of the filters, used in the image acquisitionsystem, it is possible to predict a vector of image values for a givenpoint in parameter space. This can be expressed asr=(i₁, i₂, . . . , i_(M)) i∈Iwhere the space I defines all possible measurements made by the opticalsystem. Using an appropriate definition of image ratios, such as on theone given above, it is possible to obtain a vector of image ratios. Thiscan be expressed asr=(r₁, r₂, . . . , r_(N)) r∈Rwhere the space R defines all possible image ratios that can be obtainedfrom the space of image measurements. A function ƒ can now be definedwhich maps from points in parameter space to points in the space ofimage ratios. To implement this function it is first necessary tocompute the spectral reflectance of the material of interest for thegiven set of parameter values, or point in parameter space. Using thisspectral reflectance, along with the spectral responses each of thefilters R^(n)(λ), a vector of image values can be calculated. Finallyfrom this a vector of ratios can be obtained. This three-stage mappingcan written asƒ:P→Rto denote the mapping from parameters space to the space of imageratios. Provided that a remittance spectrum can be defined for anypossible parameter combination then this mapping is defined for thewhole or parameter space. The proposed invention deals with the inverseof this function, defined asg:R→Pwhich denotes the mapping from the space of image ratios back toparameter space. A key part of the invention is to establish whether asuitable function g can be defined which will allow any measured ratioto be mapped back to the appropriate parameter combination. Such amapping must be 1-1. That is, for every point in the space of imageratios there must be a corresponding unique point in parameter space. Ifthis is not the case, ambiguity will arise as it could be possible torecover more that one set of parameter values from a given vector ofimage ratios. To establish this condition, it is first necessary to dealwith the function ƒ, which must be considered a vector valued functionof a vector variable, that is,r=ƒ(p).

To establish whether this function is 1-1 the determinant of theJacobian matrix, corresponding to this mapping, can be analysed. This isdefined as $J = {\begin{pmatrix}\frac{\partial f_{1}}{\partial p_{1}} & \frac{\partial f_{1}}{\partial p_{2}} & \cdots & \frac{\partial f_{1}}{\partial p_{K}} \\\vdots & \vdots & \cdots & \vdots \\\frac{\partial f_{N}}{\partial p_{1}} & \frac{\partial f_{N}}{\partial p_{2}} & \cdots & \frac{\partial f_{N}}{\partial p_{K}}\end{pmatrix} = {\begin{pmatrix}\frac{\partial r_{1}}{\partial p_{1}} & \frac{\partial r_{1}}{\partial p_{2}} & \cdots & \frac{\partial r_{1}}{\partial p_{K}} \\\vdots & \vdots & \cdots & \vdots \\\frac{\partial r_{N}}{\partial p_{1}} & \frac{\partial r_{N}}{\partial p_{2}} & \cdots & \frac{\partial r_{N}}{\partial p_{K}}\end{pmatrix}.}}$

If the determinant of this matrix is non-zero at a point in parameterspace then there exists a neighbourhood around this point where thefunction ƒ can be approximated linearly. This means that any pointswithin this region will map under a 1-1 mapping to a unique point inparameter space. If, when using a system to image a given tissue, it canbe established that the Jacobian is non-zero across the whole ofparameter space then the function ƒ will be 1-1 everywhere.

Once this condition has been established it is necessary to find eitheran approximation or an exact analytic expression for the function gwhich will enable image ratios to be mapped to specific parameters.Although in some cases it may be possible to obtain an analyticfunction, in most cases it will be necessary to construct a piecewisecontinuous approximation. This can be achieved by discretising parameterspace in suitably small intervals and generating the corresponding imageratio values for every point within a discretised space. Some form ofmultidimensional interpolation technique, such as a cubic spline, isthen used to construct a continuous piecewise approximation to thefunction g. This then allows processing of pixels from an imaged tissueto give the corresponding set of parameter values. Any number of pixelsmay be processed in this way to produce a number of parametric maps,which give quantitative information on the parameters of interest acrossthe whole of the imaged scene.

Such maps are of immense value to clinicians and other personsinterested in the composition of specific tissues.

The implementation of the proposed invention proceeds along thefollowing steps:

-   -   1. For the tissue to be imaged identify all parameters whose        variation could cause a change in spectral remittance when        illuminated with light.    -   2. Have, by some means, a method for predicting the spectral        remittance of a given tissue for any combination of the        identified tissue parameters.    -   3. Establish the spectral responses of each channel of the given        imaging system and from this define an appropriate set of image        ratios.    -   4. Check that the mapping from the space of parameters to the        space of image ratios is 1-1 over the range of all parameter        variation.    -   5. If this condition holds obtain some function, either exact or        approximate, which maps points in the space of image ratios to        the corresponding point in parameter space.    -   6. Using this function images can then be processed to give        quantitative information on the underlying tissue histology.

According to a third aspect of the invention there is provided apparatusfor analyzing at least one parameter of a body component, comprising alight source for illuminating the component with light of at least afirst and second predetermined waveband, a photoreceptor for receivinglight of at least said first and second predetermined wavebands remittedby the component reflected by the surface at a photoreceptor; surfacereflection elimination means for eliminating light reflected by thesurface of the component, where the predetermined wavebands are chosensuch that the component parameter is a one to one function of the ratiobetween the amount of light remitted by the component of the firstpredetermined wavebands and the amount of light remitted by thecomponent of the second predetermined waveband, and microprocessor meansfor analyzing the light received at the photoreceptor to provide a ratiobetween the light of the first waveband and the light of the secondwaveband, and from this calculating the component parameter.

The wavebands having image ratios which map 1-1 to a parameter ofcomponent vary depending upon the particular component, and theparticular parameter to be analysed.

Typically the method and apparatus are used to analyse all theparameters required to characterize a particular component, with thelight source and photoreceptor emitting and receiving for eachparameter, a pair of wavebands chosen such that the ratio between theamounts of light remitted by the component of each waveband (ie theimage ratio for that pair of wavebands) is a 1-1 function of theparticular parameter. In practice, the minimum number of wavebands to bemonitored will be equal to n+1, where n equals the number of parameters.

It has been found for skin that three parameters characterize thetissue, namely skin thickness, melanin concentration and bloodconcentration and melanin and blood concentration may be analysedeffectively using the methods and apparatus of the invention.

The required predetermined wavebands may be found using the methoddescribed above iteratively.

According to a fourth aspect of the invention, there is provided amethod of deriving a pair of predetermined wavebands suitable for use inanalysing a given parameter of a body component, the method comprisingthe steps of:

-   -   1) defining a set of potential wavebands    -   2) defining one or more image ratios, the or each image ratio        for a region being obtained by dividing the amount of light        remitted by the component of a given waveband for that region,        the “image value” for that filter, by another image value for        that same region;    -   3) for a component parameter to be analysed and for said defined        set of potential wavebands and for said given image ratios,        obtaining a function mapping points in parameter space to points        in image ratio space;    -   4) determining whether the mapping function provides a 1:1        correspondence between points in parameter space and points in        image ratio space; and    -   5) if the mapping function does not provide a 1:1        correspondence, rejecting said potential wavebands, repeating        steps 1) to 4) and, if the mapping function does provide a 1:1        correspondence accepting the potential wavebands as a candidate        set of predetermined wavebands.

The key step in the present invention is that of identifying a set offilter properties and image ratio and a mapping function which mapsimage ratios to tissue parameters with a 1:1 correspondence. This firststep may require consideration of many potential filter properties andcorresponding mapping functions.

Preferably, for each filter the method of the present invention is usedto determine the centre wavelength of the filter. The method mayadditionally be used to determine the full width half maximum (FWHM) ofthe filter characteristic.

Preferably, step 3) comprises constructing a Jacobian matrix for themapping function with respect to said parameter(s), and obtaining thedeterminant of that matrix. If the determinant is strictly positive orstrictly negative over the entire parameter space, then a 1:1correspondence between points in parameter space and points in imageratio space is assumed. It will be appreciated that these operations maybe performed using multiple processing steps or may be combined into asingle processing step.

Embodiments of the present invention may involve the calculation of anerror, indicative of the accuracy of parameter recovery obtained usingsaid mapping function. The error may be calculated as follows:

-   -   a) calculate the error associated with image acquisition for        each vector of each image ratio;    -   b) from the image ratio vector error, calculate the maximum        possible error in each component of the parameter vector across        the whole of parameter space; and    -   c) use the vector of parameter errors at each point within        parameter space to measure the accuracy of parameter recovery.

Alternatively corrections may be made for error by standard mathematicalerror correction algorithms the choice of which will be apparent to theskilled addressee of the specification.

The present invention may be incorporated into many different filterproperty calculation schemes. For example, in a scheme using a geneticalgorithm, the method may be used to identify a plurality of candidatefilter parameter sets. The method of the present invention is thenapplied repeatedly to find an optimal filter parameter set using thecandidates.

Alternatively, the method may be employed in a scheme using a gradientdescent algorithm. In such a scheme, the method of the third aspect ofthe present invention is employed to identify a first candidate set offilter parameters. This set is then used to make a selection of anotherset of filter properties, and the process repeated as often as necessaryto arrive at an optimal solution. Of course, any suitable optimizationalgorithm can be used to compute an optimal solution or a solution whichhas sufficient accuracy.

Each time the method steps 1) to 4) are carried out, the image ratiosmay or may not be changed. That is to say that, for each repetition, thepotential wavebands and the image ratios may be changed, or only thepotential wavebands may be changed.

Although this invention is applicable with particular advantage to thenon invasive analyzing of tissue—typically animal and preferably humantissue it will be appreciated that the method and apparatus could alsobe used to monitor parameters of a material where the parameterscharacterizing the material have wavelength specific optical propertiesand where it is possible to control the spectral characteristics of theillumination.

According to a fifth aspect of the invention there is provided a methodof determining a property or properties of each of a set of filters,which filters are used to select specific wavelength ranges to quantifya parameter or parameters of a tissue, the method comprising the stepsof:

-   -   1) defining a set of potential filter properties    -   2) defining one or more image ratios, the or each image ratio        for a region being obtained by dividing the quantified output of        a given filter for that region, the “image value” for that        filter, by another image value for that same region;    -   3) for an object or material to be analysed and for said defined        set of potential filter properties and for said given image        ratio, obtaining a function mapping points in parameter space to        points in image ratio space;    -   4) determining whether the mapping function provides a 1:1        correspondence between points in parameter space and points in        image ratio space; and    -   5) if the mapping function does not provide a 1:1        correspondence, rejecting said potential filter properties,        repeating steps 1) to 4) and, if the mapping function does        provide a 1:1 correspondence accepting the potential filter        properties as a candidate set of filter properties.

According to a sixth aspect of the present invention there is providedapparatus for analysing an object or material having means forconducting a spectral analysis of remitted, emitted, and/or transmittedlight to quantify a parameter or parameters of an object or material,the apparatus comprising a plurality of filters for splitting said lightinto respective components, the filters having properties obtained byusing the method of the above first aspect of the invention.

It will be appreciated that the filters of the apparatus may beimplemented in optical, electrical electronic, or software form.

BRIEF DESCRIPTION OF THE DRAWINGS

Methods and apparatus according to the various aspects of the inventionwill now be described, by way of example only with reference to theaccompanying drawings, in which:

FIG. 1 illustrates a function ƒ which maps an image ratio {overscore(i)} to a material parameter p;

FIG. 2 illustrates a combination of errors in parameter space, mapped toimage ratio vector space;

FIG. 3 illustrates a model of the layered structure of skin;

FIGS. 4 a and 4 b show how the remitted spectrum (intensity vswavelength) varies for different melanin and blood levels respectively;

FIG. 5 illustrates a set of filters suitable for analysing blood andmelanin levels in skin;

FIG. 6 is a flow diagram illustrating a method of defining a set offilter properties for use in analysing the properties of an object ormaterial;

FIG. 7 is a flow diagram illustrating a method of defining a set ofsuitable wavebands for use in analyzing the parameters of tissue;

FIG. 8 is a schematic view of a method and apparatus for analyzingfacial skin; and,

FIGS. 9 a, 9 b and 9 c are respectively, a colour image of a human facetaken with a standard digital camera and parametric maps, showing agrey-scale representation of then quantitative measurements of melaninand blood derived using the method and apparatus in accordance with thesecond and third aspect of the invention.

The proof of the theory behind the selection of appropriate wavebandsand image ratios for a given parameter will now be described withreference to FIGS. 1,2 and 6

In a typical analysis system, light remitted from an object can bemeasured using a digital camera with a small number of optical filtersrepresenting a number of wavebands. Image values—brightness or“intensity”—for each image location (x, y) for a given filter (the nthfilter) are given by: $\begin{matrix}\begin{matrix}{{i^{n}\left( {x,y} \right)} = {{K_{b}C_{b}^{n}} + {K_{s}C_{s}^{n}}}} \\{= {{K_{b}{\int{{E(\lambda)}{S(\lambda)}{R^{n}(\lambda)}{\mathbb{d}\lambda}}}} + {K_{s}{\int{{E(\lambda)}{R^{n}(\lambda)}{\mathbb{d}\lambda}}}}}}\end{matrix} & (2)\end{matrix}$where K_(b) and K_(s) are the geometric terms of the body and surfacecomponents respectively and C_(b) ^(n) and C_(s) ^(n) are colour terms.The first integral in equation (2) is the product of three terms: E(λ)is the illuminating light, S(λ) is the spectral remittance from the bodyof the imaged object, and R^(n)(λ) is the spectral response of the nthoptical filter. In the second integral there are only two terms as thereis no wavelength dependence on the surface component of reflection. Thedichromatic reflection model is very important for 3-D scene analysis asit allows for both colour and geometrical analysis of objects within ascene.

A key issue is to show that the technique proposed here is valid forproblems where the intensity of the illuminating light is unknown(whilst assuming that the spectral definition of the illuminating lightis known). For this purpose the incident light is written as:E(λ)=ε₀ E ₀(λ)  (3)where ε₀ is a wavelength independent scaling factor. Equation (2) nowbecomesi ^(n)(x, y)=ε∫E ₀(λ)S(λ)R ^(n)(λ)dλ  (4)where ε=ε₀K_(b). A digital camera records an N-dimensional vector ofimage values at each location (x; y). If a mapping, which is independentof the constant ε, can be established between the vector of image valuesand the vector of parameters, then it will be possible to recover sceneparameters from image data in a way that does not depend on illuminationintensity or scene geometry.

We now introduce the concept of an image ratio, obtained by dividing oneimage value, calculated from equation (4), by another. For a given imagevector, the nth image ratio is given as: $\begin{matrix}{\overset{\_}{i^{n}} = {{\frac{i^{n}}{i^{m}}\quad n} \neq {m.}}} & (5)\end{matrix}$

Simple consideration of equation (4) shows that any ratio defined inthis way will be invariant to a change in the parameter ε. Thus anymethod for the recovery of parameter values from image ratios will beindependent of scene geometry and illumination intensity.

The objective here is to extract quantitative parameters upon which theobject colouration depends, not to find statistical similarities.Moreover, the specific filters are chosen to maximise the distance inthe image ratio space between vectors corresponding to similar parametervalues, as this minimises the error on the parameter value recoveredfrom the colour image.

The technique described is generally applicable to scenes in which asmall number of parameters are required to describe all possible objectsobject characteristics. In the formulation, the parameters will beconsidered to vary continuously. Thus, the technique will beparticularly applicable to problems where object characteristics need tobe measured across an image. For example a medical imaging system may berequired to analyse a particular tissue. The underlying structure of thetissue will not vary, only specific characteristics such as thickness ofthe different layers (including zero thickness) or the concentration ofa particular chemical constituents (including zero concentration). Inthis situation a small parameter vector can describe all possiblevariations in the characteristics of the imaged scene. For K sceneparameters the parameter vector is defined as: $\begin{matrix}{p = {{\sum\limits_{k = 1}^{K}{p_{k}\quad p}} \in P}} & (6)\end{matrix}$and the space P defines all potential object characteristics.Ultimately, a mapping from image ratios back to the parameter vector isrequired, but first the forward problem of obtaining image ratios for agiven parameter vector is considered. A reflectance spectrum,corresponding to a given point within parameter space, can be describedby the vector in M dimensional wavelength space: $\begin{matrix}{\lambda = {{\sum\limits_{m = 1}^{M}{\lambda_{m}\quad\lambda}} \in \Lambda}} & (7)\end{matrix}$where the space Λ defines all possible spectral reflectance functions.The mapping a, defined asa:P→Λ  (8)is introduced to denote the mapping from parameter space to wavelengthspace. This mapping gives the spectral reflectance of the objectspecified by the vector p. Such a mapping can be achieved either by aspectroscopic measurement, or by using a mathematical model which takesas input the parameters and produces a corresponding reflectancespectrum. Models of light propagation in different media, such as theMonte Carlo method or the Kubelka Munk approximation, can be used forthis purpose. It must be possible to perform this mapping across thewhole of parameter space, thus defining every possible spectralreflectance function.

A digital camera with N optical filters records an N-dimensional imagevector at each pixel. The image vector is given as: $\begin{matrix}{i = {{\sum\limits_{n = 1}^{N}{i^{n}\quad i}} \in I}} & (9)\end{matrix}$where I describes the space of all possible image values. The process ofimage acquisition can be considered as the projection of points inwavelength space to points in filter space. This projection is performedby the mapping function:b:Λ→I.  (10)

Equation (4) performs this mapping b in continuous form. In discreteform, the response of the nth optical filter, is given as:$\begin{matrix}{i^{n} = {\varepsilon{\sum\limits_{m = 1}^{M}{R_{m}^{n}\lambda_{m}}}}} & (11)\end{matrix}$where λ_(m)=E₀(λ)S(λ) and the positive weights at each wavelength aregiven by R_(m) ^(n), thus defining each filter response function. Adigital camera effectively performs the mapping b, projecting pointsfrom a large dimensional space (wavelength space) to a small dimensionalspace (filter space). With such a mapping there will be a substantialloss of information. However, even with this loss of information, itshould be possible to define the mapping in such a way that accurateinformation regarding the original parameter values can still berecovered from image data. Conditions for this mapping will be discussedin the following later.

Most current image acquisition systems use an RGB system of filters.Although this defines a potential mapping b, it may not be the bestmapping with which to recover parameter values from image data. However,it is known to select specific filters to obtain better clarity of datathan that possible with an RGB system (although mainly for visualizationor image segmentation, not for quantification). Also, in spectrometry,particular spectral wavelengths are selected using statistical methodsto improve quantification of components in mixtures. It will thereforebe appreciated that an objectively defined set of optical filters isable to perform the task of recovery of parameters, which describe thevariation in human skin, better than a standard RGB system.

Once the vector of image values has been obtained, a vector of imageratios can be calculated using equation (5). The vector of image ratiosis given as: $\begin{matrix}{\overset{\_}{i} = {{\sum\limits_{\overset{\_}{n} = 1}^{\overset{\_}{N}}{\overset{\_}{i^{n}}\quad\overset{\_}{i}}} \in \overset{\_}{I}}} & (12)\end{matrix}$where {overscore (I)} describes the space of all possible image ratios.The mapping from filter space to the space of image ratios is performedafter image acquisition and will be referred to as mapping c, definedas:c:I→{overscore (I)}.  (13)

There are many ways to define the image ratios and thus the mapping c.For example, pairs of image values could be used to define image ratiosas: $\begin{matrix}{{{\overset{\_}{i}}^{n} = {{\frac{i_{{2n} - 1}}{i_{2n}}\quad n} = 1}},2,\ldots\quad,\frac{N}{2}} & \left( 14 \right.\end{matrix}$or a single image value could be taken as the denominator with which tocalculate image ratios from the remaining image values, for example:$\begin{matrix}{{{\overset{\_}{i}}^{n} = {{\frac{i_{n}}{i_{1}}\quad n} = 2}},3,\ldots\quad,{N.}} & (15)\end{matrix}$

At most the dimensionality, {overscore (N)}, of the new space will beone less that that of the original filter space, N. This wouldcorrespond to the definition given in equation (15). Alternatively, ifthe image ratios were defined as given in equation (14), then thedimensionality of the new space will be half that of the original filterspace. The aim is to recover a K-dimensional parameter vector from{overscore (N)} image ratios. Thus there must be at least as many imageratios as parameters, that is, {overscore (N)}≧K.

The function ƒ defined as:ƒ=a∘b∘c ƒ:P→{overscore (I)}  (16)represents the three stage mapping from parameter space to wavelengthspace, to image space, and finally to the space of image ratios. For agiven set of optical filters, it will be possible to perform thismapping across the whole of parameter space, provided that it ispossible to obtain a spectrum for any given parameter vector. Theinverse of function ƒ is defined as:ƒ⁻¹:{overscore (I)}→P  (17)and maps from the space of image ratios directly to parameter space. Ifit is possible to define an appropriate ƒ⁻¹, it will be possible torecover parameter values from image data in a way that is independent ofillumination intensity and scene geometry. The ultimate aim is to findthe optimum ƒ⁻¹ which maximises the accuracy of parameter recovery.Before a detailed discussion of this mapping is presented, it isimportant to emphasise that the form of the function ƒ will depend onthe mappings a, b and c. Although mapping a is fixed for a givenproblem, mapping b will vary with the choice of optical filters andmapping c will vary depending on how the image ratios are defined.

Any mapping function which is to map from the space of image ratios({overscore (I)}-space) to parameter space (P-space) must be 1 to 1.That is, for a given point in P-space, there must be a correspondingunique point in {overscore (I)}-space and vice-versa. If this is not thecase, ambiguity will arise as it could be possible to recover more thatone set of parameter values from a given vector of image ratios. Oncethis condition has been established, it is necessary to consider theerror associated with parameter recovery as, using a digital camera, itwill only be possible to obtain image values to within a givenuncertainty. This will introduce an uncertainty into the final recoveryof the parameter vector. There could also be an error associated withthe prediction measurement of a spectrum from the parameter vector. Forsimplicity the analysis presented here will be restricted to problems inwhich the error associated with the spectral measurement can beneglected.

Initially, the problem where one parameter is sufficient to describe allvariation in an imaged scene will be analysed. The methodology will thenbe extended to problems where the number of parameters is greater thanone.

Consider the case where one image ratio (two image values) is used torecover a single parameter value. FIG. 1 illustrates a function ƒ whichgives the image ratio as a function of the parameter p. It is clear thatin order to satisfy the 1 to 1 condition, the curve must not have anyturning points: that is, it must increase or decrease monotonically inthe appropriate range of p. Mathematically this is expressed as:$\begin{matrix}{{\frac{\mathbb{d}f}{\mathbb{d}p}} > {0\quad{\forall{p \in {P.}}}}} & (18)\end{matrix}$

Measurement of an image ratio value {overscore (i)}₀, corresponding to aparameter value p₀, is now considered. Associated with acquisition ofeach image value is an uncertainty due to camera error. It isstraightforward to show, using standard error analysis, that the errorassociated with an image ratio {overscore (i)}, which has beencalculated from the two image values i₁ and i₂, is given as:$\begin{matrix}{{\Delta\quad\overset{\_}{i}} = {\Delta\quad{i\left( \frac{i_{1} + i_{2}}{i_{2}^{2} - \left( {\Delta\quad i} \right)^{2}} \right)}}} & (19)\end{matrix}$where Δi is the camera uncertainty. This error has been shown on theordinate of the graph in FIG. 1. If the derivate of ƒ is non-zero insome neighbourhood of p₀ then it is possible to approximate thisfunction linearly. Assuming the error Δi to lie within thisneighbourhood, the corresponding error in the parameter value is givenas: $\begin{matrix}{{\Delta\quad p} = {\Delta\quad{\overset{\_}{i}/{\frac{\mathbb{d}f}{\mathbb{d}p}.}}}} & (20)\end{matrix}$

Thus, it is possible to obtain a value for the error Δp, associated withparameter recovery, at any point in P-space. An optimisation criterioncan then be defined based on some measure of this error. For mostapplications it will be necessary to minimise the error equally acrossthe whole of P-space. For others it may be that high accuracy parameterrecovery is required within a certain range of parameter values. Forexample, in a medical image application, imaged tissue could be deemedpathological once a characterising parameter changes beyond a thresholdlevel. This would need to be accounted for with some form of weightingin the optimisation criterion. It is interesting to note that in orderto minimse Δp, it is necessary to maximise the magnitude of thederivative given in equation (18). This will ensure that any search,carried out to find an optimum ƒ, will tend to move towards regions ofsearch space where the 1 to 1 condition is satisfied.

In theory it is possible to recover the parameter using more than oneimage ratio. In this case it will be necessary to calculate the errorassociated with parameter recovery for each of the image ratios andselect the one, at each point in P-space, which has the smallestassociated error (Δp). It may be that the optimisation procedure gives asingle image ratio which performs better than any other across the wholeof P-space. In this situation there is no benefit to using more that oneimage ratio.

The analysis is now extended to the general problem where the recoveryof a K-dimensional parameter vector is required from an {overscore (N)}dimensional vector of image ratios. Initially the analysis will berestricted to the case where {overscore (N)}=K and will then be extendedto include situations where {overscore (N)}>K. As discussed earlier, if{overscore (N)}<K, then it is not possible to recover K-dimensional datafrom an {overscore (N)} dimensional measurement.

The mapping function f, defined as:{overscore (i)}=f(p)  (21)must now be considered a vector valued function of a vector variable. Inthe following analysis specific results from differential geometry willbe used. For further details the reader is directed to for example M. M.Lipschutz, Differential geometry (McGraw-Hill Book Company, New York,1969). To establish whether the function ƒ provides a 1 to 1relationship, it is first necessary to consider the behaviour of thedeterminant of the Jacobian matrix, simply referred to as the Jacobian.This is defined as: $\begin{matrix}{{\det\left( \frac{\partial f_{n}}{\partial p_{k}} \right)} = {{\begin{matrix}\frac{\partial f_{1}}{\partial p_{1}} & \frac{\partial f_{1}}{\partial p_{2}} & \cdots & \frac{\partial f_{1}}{\partial p_{k}} \\\cdots & \cdots & \cdots & \cdots \\\frac{\partial f_{n}}{\partial p_{1}} & \frac{\partial f_{n}}{\partial p_{2}} & \cdots & \frac{\partial f_{n}}{\partial p_{k}}\end{matrix}}.}} & (22)\end{matrix}$

The Jacobian can be considered the multidimensional equivalent of theone dimensional derivative given in equation (18). The inverse functiontheorem states that, if the Jacobian is non-zero at a point p₀ inP-space, then there exists a neighbourhood around p₀ where the functionf can be approximated linearly asf(p)=f(p ₀)+df(p ₀)(p−p ₀)  (23)where df is the differential of f and is given as: $\begin{matrix}{{df} = {{\frac{\partial f}{\partial p_{1}}{dp}_{1}} + {\frac{\partial f}{\partial p_{2}}{dp}_{2}} + \ldots + {\frac{\partial f}{\partial p_{k}}{{dp}_{k}.}}}} & (24)\end{matrix}$

It follows that in this neighbourhood the function f provides a 1 to 1relationship. Thus, if it is possible to establish that the Jacobian isstrictly positive or strictly negative throughout the whole of P-space,the function f will be 1 to 1 everywhere. Once this condition has beenestablished, it is necessary to consider how the error associated withimage acquisition maps under f⁻¹, to give the corresponding error inparameter recovery. The error associated with each image ratio iscalculated using equation (19). The combination of errors maps out ahypervolume in {overscore (I)}-space, centred on the point i₀. This hasbeen illustrated in FIG. 2 for the case of a 2D P-space, where anellipse is obtained (or a circle if the errors are equal). An ellipsoidis obtained in 3D space and a hyperellipse in higher dimensions.Although the following analysis will be based on a 2D P-space, thearguments are equally valid in higher dimensions.

The ellipse in {overscore (I)}-space represents all possible image ratiovectors which could correspond to a camera measurement {overscore(i)}={overscore (i)}₀. It is assumed that the region of error lieswithin the neighbourhood of {overscore (i)}={overscore (i)}₀ where themapping function f can be approximated linearly. Thus, under the mappingf⁻¹, the ellipse in {overscore (I)}-space maps directly to anotherellipse in P-space. This new ellipse is centred on the point p=p₀ andrepresents all possible parameter vectors which could be recovered fromthe vector of image ratios {overscore (i)}={overscore (i)}_(o). Theerror associated with parameter recovery is obtained by considering theworst case scenario: that is the point within the ellipse in P-spacewhich is at the maximum distance from the point p=p₀. This maximumdistance must be calculated separately for each component, p_(k), of theparameter vector to obtain the error associated with recovery of eachindividual component. To calculate these errors it is necessary toconsider how the ellipse is transformed under the mapping f⁻¹, which islinear provided the Jacobian is non-zero.

Under a linear mapping the ellipse will be translated, scaled androtated. The translation associated with the linear mapping defines thepoint p=p₀ which is mapped to from the point {overscore (i)}={overscore(i)}₀. The two other transformations, scaling and rotation, are bestunderstood by considering how a vector d{overscore (di)}=df in{overscore (I)}-space, maps under f⁻¹ to give a corresponding vector dpin P-space. The vector dp can be calculated from the inverse form ofequation (24) which, in matrix form, is given as:dp=J⁻¹d{overscore (i)}  (25)where J denotes the Jacobian matrix. Note that J⁻¹ exists only if theJacobian in non-zero. This must be the case if the 1 to 1 condition isto be satisfied.

The vectors A and B correspond to the major and minor axes of theellipse in {overscore (I)}-space and are given as: $\begin{matrix}{A = {{\begin{pmatrix}{\Delta\quad{\overset{\_}{i}}_{1}} \\0\end{pmatrix}\quad B} = {\begin{pmatrix}0 \\{\Delta\quad{\overset{\_}{i}}_{2}}\end{pmatrix}.}}} & (26)\end{matrix}$

Under the mapping f⁻¹ these vectors map to the vectors A′ and B′ whichcorrespond to the major and minor axes of the ellipse in parameterspace. Solving equation (25) for each of these vectors gives:$\begin{matrix}{A^{\prime} = {{\begin{pmatrix}{\Delta\quad p_{1}^{A}} \\{\Delta\quad p_{2}^{A}}\end{pmatrix}\quad B^{\prime}} = \begin{pmatrix}{\Delta\quad p_{1}^{B}} \\{\Delta\quad p_{2}^{B}}\end{pmatrix}}} & (27)\end{matrix}$where Δp₁ ^(A) and Δp₂ ^(A) are the components of the vector A′ in thedirection of p₁ and p₂ respectively. Similarly, Δp₁ ^(B) and Δp₂ ^(B)are the components of the vector B′ in the direction of p₁ and p₂respectively. To calculate the error in each component of the parametervector it is necessary to consider the worst case scenario. It can beseen from FIG. 2 that this corresponds to taking the maximum of Δp₁ ^(A)and Δp₂ ^(B) as the error in p₁ and taking the maximum Δp₂ ^(A) and Δp₂^(B) as the error in p₂. This error can be specified by a vector Δp andcan be calculated for any given point in parameter space. With thismeasure of the accuracy of parameter recovery across the whole ofparameter space, it is possible to define an optimnisation criterion.This could simply be based on a sum of the errors at every point inP-space or could be chosen to favour accuracy of recovery of a subset ofthe original parameters. Once this optimisation criterion has beendefined, a search can be used to find the optimum mapping function f. Itis important to note that, although the above discussion is based on a2D parameter space, the methodology is equally applicable to anyK-dimensional parameter space.

An algorithm for the implementation of the proposed methodology is givenas follows:

-   -   1. Establish a suitable search space from a parameterisation of        mappings b and c.    -   2. For a given mapping function f calculate the vector of image        ratios for each point within a discretised parameter space.    -   3. For each point, check that the Jacobian is either strictly        positive or strictly negative across the whole of parameter        space. If this condition is held then compute the inverse of the        Jacobian matrix. If not then return to step 1 and define a new        mapping function f.    -   4. Using equation (19), calculate the error associated with        image acquisition for each vector of image ratios.    -   5. From the image ratio vector error calculate the maximum        possible error in each component, p_(k), of the parameter vector        across the whole of parameter space.    -   6. Use the vector of parameter errors at each point within        parameter space to measure the accuracy of parameter recovery.    -   7. Repeat steps 2-6 with some optimisation technique which        enables an optimum mapping function f to be determined.

It is fairly straightforward to extend this methodology to the case inwhich {overscore (N)}>K: that is, where there are more image ratios thanparameter values. Initially every possible K-dimensional subspace ofimage ratios will need to be defined from the original {overscore(N)}-dimensional space of image ratios. It will then be necessary to gothrough the above procedure for each potential subspace and obtain thevector of parameter errors at each point within parameter space. Toachieve the maximum possible accuracy the best Δp must be selected atevery location within parameter space. Thus every point in P-space willbe linked to a specific image ratio combination. It will then benecessary to link every region of the original {overscore(N)}-dimensional space of image ratios to the particular subspace ofimage ratios which should be used for parameter recovery. It isimportant to note that it is necessary to recover the whole parametervector at each point {overscore (i)}₀ within a particular K-dimensionalsubspace of image ratios. It is not possible to attempt to improve theaccuracy of the system by recovering different components of theparameter vector from different K-dimensional subspaces of image ratios.This is mathematically invalid.

The mapping function f is a composite function of three separatemappings. Although the first mapping a, from parameter space towavelength space, is fixed for a given problem, mappings b and c canvary depending on the choice of optical filters and definition of imageratios. Thus, to define an appropriate search space it is necessary toparameterise mappings b and c. Mapping b, which represents imageacquisition, is defined by the positive N×M matrix R_(m) ^(n), given inequation (11). Typically this matrix will contain many elements and anappropriate parameterisation should be based on typical filter responsefunctions. For example, the position of the central wavelength and ameasure of width could be used to define a Gaussian shape.

Parameterisation of the mapping function c will be fairlystraightforward as there are only a limited number of ways of combiningimage values to produce independent image ratios. In some applicationsthe form of this mapping may be fixed apriori. Thus, it will notincrease the overall dimensionality of the search space.

An optimisation method should search the whole space of possiblemappings using the optimisation criterion outlined in the previoussection. One technique which is ideally suited to this type of search isa genetic algorithm, GA, {see T. Back and H. P. Schwefel, “An overviewof evolutionary algorithms for parameter optimisation,” EvolutionaryComputation 1, 1-23 (1993)} as it is straightforward to define a fitnessfunction which measures the accuracy of parameter recovery. Geneticalgorithms have been shown to work well on a wide range of problems withobjective functions that do not possess “nice” properties such ascontinuity, differentiability or satisfaction of the Lipschitz Condition{see L. Davis, The handbook of genetic algorithms (Van NostrandReingold, New York, 1991), and D. Goldberg, Genetic algorithms insearch, optimization and machine learning (Addison-Wesley, London,1989)}.

The above techniques will now be further exemplified by consideringtheir application to the analysis of a body component, in this case anormal skin composition. Firstly, the prediction of spectral reflectanceis considered.

In order to perform mapping a it is necessary to have either amathematical model which can predict spectral reflectance for a givenset of parameter values or some technique for measurement of theappropriate spectrum. For this application we use the mathematical modeldeveloped by Cotton and Claridge {see S. D. Cotton and E Claridge,“Developing a predictive model of human skin colouring,” Proc. of SPIEMed. Imag. 2708, 814-825 (1996)}. With this model it is possible topredict the spectral reflectance for a given set of parameters. Anoutline of the model is now given.

Skin can be considered to be the four-layer structure depicted in FIG.3. A negligible amount of light is reflected from the surface of theskin, thus the surface term in equation (2) can be neglected. Althoughnot absorbing any radiation, the stratum corneum scatters the incomninglight in all directions. Light which penetrates this layer can thus beconsidered diffuse. In the epidermis light is absorbed by the pigmentmelanin. The absorption at each wavelength can be calculated using theLambert-Beer law and will depend on the product of the melaninextinction coefficient and the pigment concentration. After passingthrough the epidermis the light is both scattered and absorbed by thepapillary dermis. The absorption results from the presence of blood andscattering from the underlying collagen structure. The simple Kubelka-Munk light theory {P. Kubelka and F Munk, “Ein Beitrag zur Optik derFarbanstriche”, “Z. Tech. Opt” 11, 593-611 (1931)} can be used to modelthe interaction of light with the papillary dermis as the necessarycondition of diffuse incident illumination is satisfied. Any light whichpasses through the papillary dermis into the recticular dermis can beneglected as no significant backscattering occurs in this layer. Usingthis two-layer light transport model it is possible to obtain theremitted spectra for given concentrations of melanin and blood. A moredetailed description of this model can be found in S. D. Cotton and EClaridge, “Developing a predictive model of human skin colouring”, Proc.of SPIE Med. Imag. 2708, 814-825 (1996).

For a given papillary dermal thickness, changes in melanin and bloodcharacterise all histological variation and thus define a 2-D parameterspace for healthy skin. To carry out the optimisation proceduredescribed above it is necessary to discretise parameter space. This isdone at equal intervals to define 10×10 points, each of whichcorresponds to a spectrum generated by the mathematical model. Forsimplicity, concentration values will be denoted by a number between 1and 10. FIGS. 4 a and 4 b show how the remitted spectrum changes asmelanin and blood are varied respectively. With a change in melaninconcentration, the intensity of the whole spectrum is seen to decrease,with a more pronounced change in the blue region. As the bloodconcentration is decreased the most significant reduction in intensityis observed in the green region, the resulting shape reflecting the twoabsorption maxima of oxyhaemoglobin, a blood born pigment.

To define a suitable search space it is necessary to parameterise themappings b and c. A parameterised form of b is chosen to define atypical interference filter. This is modelled as a square profile withGaussian decay at each side. Two parameters are required to specify thisshape: the central wavelength and a full width half maximum (FWHM).Optimisation is carried out for three such filters, defining a 6-Dsearch space. With three filters giving three image values, i₁; i₂ andi₃, the only possible definition of image ratios, if we assume i₁=i₃ isequivalent to i₃=i₁, is given as: $\begin{matrix}{{\overset{\_}{i}}_{1} = {{\frac{i_{1}}{i_{3}}\quad{\overset{\_}{i}}_{2}} = {\frac{i_{2}}{i_{3}}.}}} & \left( 28 \right.\end{matrix}$

In this instance the mapping c does not increase the dimensionality ofthe search space.

The optimisation procedure was implemented following the algorithm givenabove. Initially the vector of image ratios was calculated for everypoint within the discretised parameter space. This was done using themathematical model to perform mapping a, the parameterised form ofmatrix R_(n) ^(m) to perform mapping b and the equations (28) to performmapping c. The derivative of each image ratio, with respect to eachparameter, was obtained at each point within discretised parameter spaceusing three-point finite difference approximations. The Jacobian matrixwas then constructed at every point within parameter space, andproviding its determinant was non-zero everywhere, the inversecalculated. If this condition was violated then a new mapping f wasdefined. The errors associated with image acquisition were thencalculated using equation (19). The absolute value of the error in eachimage value will vary depending on the camera gain setting. Althoughthis constant will not affect the mapping f, it must be estimated inorder to calculate the effective camera error. For this application itwas taken to be 0.78% of the maximum value of all the image valuesacross parameter space. This corresponds to a camera which has been setto give a maximum reading for the largest spectral reflectance and acamera error of two grey scale levels in an 8-bit representation.

Using the procedure outlined above the error associated with parameterrecovery in both melanin and blood was obtained for each point withinthe discretised parameter space. In order to find an optimum f, it isnecessary to minimise the errors in recovery of both melanin and bloodacross the whole of parameter space. Thus the fitness function for theGA was taken to be the sum of the errors in both melanin and blood. Thisprocedure was implemented in matlab™ using a standard GA to search thespace of available mappings.

The boundaries of the search space were chosen such that the centralwavelength was constrained to lie in the visible region (400 nm-700 nm)and such that the widths of the filters were allowed to vary from a FWHMof 25 to 200 nm. Although it is now possible to engineer almost anyshape of interference filter, this corresponds to an economically viablerange of such filters.

Although it was originally assumed that an image ratio defined as i₁/i₃would be equivalent to i₃/i₁, the results of the GA search showed thatthis was not the case. The search was intitialised for a random seedand, although the same central wavelengths were always obtained,different filters were selected corresponding to i₃ defined in equation(28). Further investigation showed that these local maxima in the searchspace corresponded to differing distributions of errors both, acrossparameter space and between the two parameters. This is because thefitness function, or measure of accuracy, was defined as the sum theerrors across parameter space for both melanin and blood. Thus, a lossof accuracy in one parameter could be compensated for with an increasein the other. It may be that, with a more exact specification of theerror distribution in the fitness function, it would be possible toobtain the same results for every GA search.

FIG. 5 shows a filter combination which gave a similar error in therecovery of both melanin and blood. The image ratios were calculated bydividing the filter centred at λ=473 nm and λ=560 nm by the response ofthe filter centred at λ=700 nm. To understand why these specific filterswere selected it is necessary to analyse the spectral curves shown inFIG. 4. The filters centred at λ=473 nm and λ=560 nnmm correspond tospectral locations where there is a large change in intensity with theparameters melanin and blood respectively. A third filter was thenrequired in a region of the spectrum in which the remitted light whichwas either significantly less or significantly more than that of theother two filters. The filter centred at λ=700 nm was chosen as italways gave the largest response at any point within parameter space.This ensured that the derivatives of each image ratio decreasedmonotonically across the whole of parameter space. The Jacobian,calculated from these derivatives, was strictly positive across thewhole of parameter space. It is interesting to note that somealternative filter combinations gave Jacobians which were strictlynegative across parameter space, corresponding to alternative localmaxima in the search space. If two filters are chosen, to define animage ratio, which vary similarly across parameter space, there will beminimal change in that image ratio and thus it will be of limited valuefor parameter measurement.

It has been demonstrated that, using an objectively defined set ofoptical filters, it is possible to recover scene parameters from imagedata in a way which is insensitive to geometry and incidentillumination. In the example problem, discussed above, the errorassociated with this parameter recovery was found to be relativelysmall. The invariance of this mapping means that the technique will beparticularly applicable to medical image applications where there issignificant curvature of the surface of the imaged tissue, such as neara joint. It also means that the method can be used for whole bodyimaging. It will also be unnecessary to calibrate the camera todetermine the intensity of the incident light. This could help tosignificantly increase the speed of image acquisition and laterprocessing.

The methodology set out here has been developed for a measurement task,where the scene parameters are known to vary continuously. The techniquecan be also be applied to problems of recognition, where it is necessaryto differentiate discrete objects based on some measure of theirspectral reflectance. This approach has been discussed in the article G.Healey, “Using colour for geometry-insensitive segmentation,” J. Opt.Soc. Am. A 6, 920-937 (1989) who used the idea of normalised colour toidentify different regions of normalised colour space corresponding todifferent metal and dielectric materials. This enabledgeometry-insensitive segmentation of an imaged object comprised of anumber of different materials.

It will be appreciated that in order to implement the proposedmethodology, a look-up table should be established between all possibleimage ratios and scene parameters. Although this may be time consuming,it is only necessary to carry out this procedure once. Once established,this look-up table will ensure no significant processing after imageacquisition, making this technique particularly suitable to real-timeapplications.

FIG. 6 is a flow diagram showing the key steps in the method describedabove.

The method and apparatus for analysing at least one parameter of a bodycomponent, in this case animal tissue in the specific form of facialskin is illustrated in FIG. 8. A light source 100 provides illuminationto the tissue and remitted light is received at photoreceptor 200 whichin this case is a digital camera. Two cross polarised linear polarisingfilters 300 are used to eliminate the effects of surface reflection fromthe skin. One filter 300 is placed between the light source 100 and theskin and the other filter 300 is placed between the skin and the digitalcamera 200.

In this case the digital camera is provided with Red, Green and Bluefilters so that light in those wavebands is received by the camera.These wavebands are used-to provide image ratios of which theconcentration of melanin and the concentration of blood are one to onefunction.

The procedure outlined in FIG. 7 was applied to image data in thefollowing way.

-   -   1. Two parameters: the concentration of melanin and blood were        identified as sufficient to describe all histological variation        of healthy tissue.    -   2. A Kubelka-Munk model of light transport was used to predict        the remitted spectrum of tissue for any given combination of        melanin and blood concentration.    -   3. The spectral responses of each of the RGB channels of the        colour camera were established and image ratios defined as        -   a. Ratio 1=Green/Red Ratio 2=Blue/Red    -   4. The mapping from the 2-D space of parameter variation to the        2-D space of image ratios was checked to ensure that is was 1-1        across the whole range of appropriate parameter variation.    -   5. A piecewise continuous approximation was constructed to        define a function relating image ratios to histological        parameters.    -   6. Images were acquired using a system of crossed polarising        filters, as described above. The experimental set up has been        illustrated in FIG. 8.    -   7. The function described in step 5 was then used to process the        image data.    -   8. Parametric maps were then produced of melanin and blood        across the imaged tissue.

In one experiment this method was applied to an image obtained using aJAI CV-M7CL+ camera imaging facial skin. Parametric maps, showing agrey-scale representation of then quantitative measurements of melaninand blood derived using this technique, are shown in FIG. 9 b and 9 c.

It should be noted that in 9b illustrating the concentration ofhemoglobin concentration across the image, spot S is identified but moleM is not identified. However in 9 c illustrating the concentration ofmelanin across the image, spot S is not identified while mole M isidentified. This illustrates simply how useful a tool this can be for aclinician.

A second specific embodiment involves the analysis of images of thehuman gastrointestinal track obtained using an endoscope. The endoscopesystem can take two alternative embodiments. In one case the endoscopeis equipped with a conventional colour camera and white light sourceequipped with cross polarizing filters¹. In a second case the endoscopeis equipped with a monochrome camera and a light source equipped withcross polarizing filters¹, with the light source that changes coloursequentially between red, green and blue, and these changes aresynchronised with the camera to produce a sequence of red, green andblue images.¹ one filter being placed between the source of illumination and thecomponent, and the other filter placed between the component and thephotoreceptor or photoreceptors with the filters being set at 90 degreesto one another.

The procedure outlined in FIG. 7 is applied to this problem, using datafrom an endoscope equipped with a conventional colour camera, asfollows:

-   -   1. Two parameters blood concentration and tissue thickness are        identified as sufficient to describe all histological variation.    -   2. A Monte Carlo model of light transport is used to predict the        remitted spectrum of the given tissue for any possible        combination of blood concentration and tissue thickness.    -   3. For an endoscope and camera system, the spectral responses of        each of the RGB channels is established and image ratios defined        as        -   a. Ratio 1=Green/Red Ratio 2=Blue/Red    -   4. The mapping from the 2-D space of parameter variation to the        2-D space of image ratios is checked to ensure that it is 1-1        across the whole range of appropriate parameter variation.    -   5. A piecewise continuous approximation is constructed to define        a function relating image ratios to histological parameters.    -   6. Images are acquired the endoscope with a system of crossed        polarising filters.    -   7. The function described in step 5 is then used to process the        image data.    -   8. Parametric maps are then produced to display variation in        blood and tissue thickness across the given image.

The procedure can be modified to analyse additional histologicalparameters with the addition of additional wavebands as described in theequations shown above. These additional wavebands may be obtained by amonochrome camera and light source with cross polarising filters takinga series of images of the subject illuminated by a sequence of colouredlights of known spectral characteristics. The spectral characteristicsof one or more of colours may lie outside the visible spectrum

1. A method of analysing at least one parameter of a body component,comprising the steps of illuminating the component or body with light ofat least a first and second waveband, receiving light of at least saidfirst and second wavebands remitted by the component at a photoreceptoror photoreceptors, and analysing the light received at thephotoreceptor(s) to provide a ratio between the amount of light remittedof the first waveband and the amount of light remitted of the secondwaveband, and from this calculating the component parameter.
 2. A methodaccording to claim 1, in which the wavebands are predetermined andcalculated by use of a mathematical model of the body component and itscharacterising parameters.
 3. A method according to claim 1, in whichthe wavebands are predetermined and derived through use of a biologicalmodel of the body component.
 4. A method of analysing at least oneparameter of a body component, comprising the steps of illuminating thebody or component with light of at least a first and second waveband,receiving light of at least said fast and second wavebands remitted bythe component at the photoreceptor(s), but eliminating light reflectedby the component or body and analysing the light received at thephotoreceptor(s) to provide a ratio between the amount of light of thefirst waveband and the amount of light of the second waveband, and fromthis calculating the component parameter.
 5. A method according to claim4 where the wavebands are chosen such that the component parameter is aone to one function of the ratio between the amount of light remitted bythe body component of the first waveband and the amount of lightremitted by the component of the second waveband.
 6. A method accordingto claim 4, in which the waveband ratios are compared with amathematically generated model of waveband ratios corresponding to arange of component parameters.
 7. A method according to claim 4, inwhich the waveband ratios are compared with an experimentally measuredset of waveband ratios corresponding to a range of component parameters.8. A method according to claims 6 where the comparison results in ameasure or measures relating to the component parameter or parameters.9. A method according to claim 4 where a function is derived relatingthe computed ratios and the component parameter or parameters.
 10. Amethod according to claim 4, in which the light reflected by thecomponent is eliminated by the use of a pair of cross polarised linearpolarizing filters, one filter being placed between the source ofillumination and the component, and the other filter placed between thecomponent and the photoreceptor or photoreceptors.
 11. A methodaccording to claim 4 in which the light illuminating the body componentis a light of a plurality of wavelengths which includes at least thewavebands.
 12. A method according to claim 11 in which tie illuminatinglight is ambient light.
 13. A method according to claim 11 in which theilluminating light is sunlight.
 14. A method according to claims 11, inwhich at last one filter is placed sequentially between the source ofillumination and the component or between the component and thephotoreceptor or photoreceptors.
 15. A method according to claim 4, inwhich the body component is human or animal tissue.
 16. A methodaccording to claim 15, in which the tissue is one of skin, the lining ofthe gut, colon, oesophagus, cervix, eye or any other epithelial tissue.17. A method according to claim 4, for analysing a plurality of bodycomponent parameters where the component is illuminated with light ofeach of a collection of wavebands. The light received by thephotoreceptor or photoreceptors includes this collection of wavebands.The light is analysed at the photoreceptor(s) to provide a collection ofratios between the amount of light of each waveband with some or all ofthe other wavebands and from this calculating the componentparameter(s).
 18. A method according to claim 4, for analysing aplurality of body component parameters in which for each componentparameter there exists a pair of predetermined wavebands such that thecomponent parameter is a one to one function of the ratio between theamount of light remitted by the component of the first predeterminedwaveband of the pair and the amount of light remitted by the componentof the second predetermined waveband of the pair, and the component isilluminated with light of each pair of predetermined wavebands, thelight received by the photoreceptor or photoreceptors is of each pair ofpredetermined wavebands remitted by the component at thephotoreceptor(s), and analysing the light received at thephotoreceptor(s) to provide for each component parameter a ratio betweenthe amount of light of the first waveband and the amount of light of thesecond waveband, and from this calculating each component parameter. 19.A method according to claim 17, in which the waveband ratios arecompared with a mathematically generated model of waveband ratioscorresponding to a range of component parameters to ascertain thecomponent values.
 20. A method according to claim 17, in which thewaveband ratios are compared with an experimentally measured set ofwaveband ratios corresponding to a range of component parameters toascertain the component values.
 21. A method according to claims 19where the comparison results in a measure or measures relating to thecomponent parameter or parameters.
 22. A method according to claims 19where a function is derived relating the computed ratios and thecomponent parameter or parameters.
 23. A method according to claim 4 inwhich the body component is skin and the parameters are theconcentration of melanin and the concentration of blood.
 24. A methodaccording to claim 23, in which the predetermined wavebands arc the Red,Green and Blue colour bands, with the three wavebands providing the tworatios which arc a one to one function with the parameters.
 25. A methodaccording to claim 4, in which the predetermined wavebands have beencalculated by the steps of: 1) defining a set of potential wavebands 2)defining one or more image ratios, the or each image ratio for a regionbeing obtained by dividing the amount of light remitted by the componentof a given waveband for that region, the “image value” for that filter,by another image value for that same region; 3) for a componentparameter to be analysed and for said defined set of potential wavebandsand for said given image ratios, obtaining a function mapping points inparameter space to points in image ratio space; 4) determining whetherthe mapping function provides a 1:1 correspondence between points inparameter space and points in image ratio space; and 5) if the mappingfunction does not provide a 1:1 correspondence, rejecting said potentialwavebands, repeating steps 1) to 4) and, if the mapping function doesprovide a 1:1 correspondence accepting the potential wavebands as acandidate set of predetermined wavebands.
 26. Apparatus for analyzing atleast one parameter of component, comprising a light source forilluminating the component with light of at least a first and secondpredetermined waveband, a photoreceptor or photoreceptors for receivinglight of at least said first and second predetermined wavebands remittedby the component reflected by the surface at a photoreceptor orphotoreceptors; surface reflection elimination means for eliminatinglight reflected by the surface or the component and means for analyzingthe light received at the photoreceptor(s) to provide a ratio betweenthe light of the first waveband and the light of the second waveband,and from this calculating the component parameter.
 27. Apparatusaccording to claim 26 where the predetermined wavebands are chosen suchthat the component parameter is a one to one function of the ratiobetween the amount of light remitted by the component of the firstpredetermined waveband and the amount of light remitted by the componentof the second predetermined waveband.
 28. Apparatus according to claim26, in which die photoreceptor comprises a digital camera.
 29. Apparatusaccording to claim 28, in which the digital camera includes a pluralityof filters, one for each predetermined waveband.
 30. Apparatus accordingto claim 26 in which the light source is ambient light.
 31. Apparatusaccording to claim 27, in which the distance between thephotoreceptor(s) and the component is between 0.5 cm and 10 m. 32.Apparatus according to claim 33, in which the distance between the lightsource and the component is between 0.5 cm and 10 m.
 33. A method forderiving a pair of predetermined wavebands suitable for use in analysinga given parameter of a body component, the method comprising the stepsof: 1) defining a set of potential wavebands 2) defining one or moreimage ratios, the or each image ratio for a region being obtained bydividing the amount of light remitted by the component of a givenwaveband for that region, the “image value” for that filter, by anotherimage value for that same region; 3) for the parameter of the componentto be analysed and for said defined set of potential wavebands and forsaid given image ratios, obtaining a function mapping points inparameter space to points in image ratio space; 4) determining whetherthe mapping function provides a 1:1 correspondence between points inparameter space and points in image ratio space; and 5) if the mappingfunction does not provide a 1:1 correspondence, rejecting said potentialwavebands, repeating steps 1) to 4) and, if the mapping function doesprovide a 1:1 correspondence accepting the potential wavebands as acandidate set of predetermined wavebands.
 34. A method according toclaim 33 and comprising, for a set of potential wavebands accepted as acandidate set of wavebands, determining the accuracy of parameterrecovery obtained using said mapping function and determining whether ornot the accuracy is sufficient or matches some other criterion.
 35. Amethod according to claim 34, wherein if the accuracy is sufficient ormatches said criterion, the candidate wavebands are adopted and if theaccuracy is not sufficient or does not match said criterion, steps 1) to5) are repeated for a different set of wavebands.
 36. A method accordingto claim 34, wherein the accuracy is determined by: a) calculating theerror associated with image acquisition for each vector of each imageratio; b) from the image ratio vector error, calculating the maximumpossible error in each component of the parameter vector across thewhole of parameter space; and c) using the vector of parameter errors ateach point within parameter space to measure the accuracy of parameterrecovery.
 37. A method according to claim 33 and comprising repeatingsteps 1) to 5) for a multiplicity of sets of potential wavebands toidentify a plurality of candidate waveband sets, determining for eachcandidate set an error value representing the accuracy of parameterrecovery obtained using the corresponding mapping function, and usingsaid candidate set as a basis for determining a preferred set ofwavebands.
 38. A method according to claim 37 and comprising using agenetic algorithm to determine a preferred set of wavebands using saidcandidate set.
 39. A method according to claim 33 and comprising using agradient descent algorithm to select an optimal set of wavebands, thestarting point for the algorithm being a first candidate set ofwavebands identified in step 4).
 40. A method according to claim 33,wherein for each waveband the method of the present invention is used todetermine the center wavelength of the waveband.
 41. A method accordingto claim 33, wherein the method is used to determine the full width halfmaximum (FEHM) of the waveband.
 42. A method according to claim 33,wherein step 3) comprises constructing a Jacobian matrix for the mappingfunction with respect to said parameter(s), and obtaining thedeterminant of that matrix.
 43. A method of determining a property orproperties of each of a set of filters, which filters are used to selectspecific wavelength ranges in a system which relies upon a spectralanalysis of remitted, emitted, and/or transmitted light to quantify aparameter or parameters of an object or material, the method comprisingthe steps of: 1) defining a set of potential filter properties; 2)defining one or more image quotients, the or each image quotient for aregion being obtained by dividing the quantified output of a givenfilter for that region, the “image value” for that filter, by anotherimage value for that same region; 3) for an object or material to beanalysed and for said defined set of potential filter properties and forsaid given image quotients, obtaining a function mapping points inparameter space to points in image quotient space; 4) determiningwhether the mapping function provides a 1:1 correspondence betweenpoints in parameter space and points in image quotient space; and 5) ifthe mapping function does not provide a 1:1 correspondence, rejectingsaid potential filter properties, repeating steps 1) to 4) and, if themapping function does provide a 1:1 correspondence accepting thepotential filter properties as a candidate set of filter properties. 44.Apparatus for analysing an object or material having means forconducting a spectral analysis of remitted, emitted, and/or transmittedlight to quantify a parameter or parameters of an object or material,the apparatus comprising a plurality of filters for splitting said lightinto respective components, the filters having properties obtained byusing the method of the claim
 43. 45. Apparatus for determining thedistribution of chromophores and/or the thickness of structural layersin a sample of epithelial tissue, the apparatus comprising: a polarizedlight source operable to illuminate a sample of epithelial tissue withpolarized light having wavelengths filling within a first, second, andthird predetermined wavebands; a polarizing filter positioned so as tofilter light remitted from a sample of epithelial tissue said polarizingfilter being such to filter out light polarized in the manner generatedby said polarized light source; an image generator operable to detectfiltered remitted light from a sample of epithelial tissue and generateimage data indicative of the intensity of filtered remitted lightreceived by said image generator having wavelengths falling within saidfirst, second and third predetermined wavebands; a ratio determinationmodule operable to process image data generated by said image generatorto determine for positions within images represented by said image data,a first ratio corresponding to the ratio of light received by said imagegenerator having wavelengths within said second waveband relative tolight having wavelengths within said first waveband, and a second ratiocorresponding to the ratio of light received by said image generatorhaving wavelengths within said third waveband relative to light havingwavelengths within said first waveband; a concentration determinationmodule operable to determine for positions within an image representedby image data generated by said image generator the concentrations ofchromophores and/or the thickness of structural layers of saidepithelial tissue at said positions in a sample of epithelial tissuerepresented by said image data utilizing said first and said secondratios determined for said positions by said ratio determination module;and an output module operable to output data representing determinedconcentrations of chromophores and/or thickness of structural layers forpoints a sample of epithelial tissue as determined by said concentrationdetermination module.
 46. Apparatus in accordance with claim 45 whereinsaid image generator comprises a digital camera.
 47. Apparatus inaccordance with claim 45 wherein said first waveband comprises awaveband corresponding to red light.
 48. Apparatus in accordance withclaim 45 wherein said second waveband comprises a waveband correspondingto green light.
 49. Apparatus in accordance with claim 45 wherein saidthird waveband comprises a waveband corresponding to blue light. 50.Apparatus in accordance with claim 45 wherein said first wavebandcomprises a waveband centered on a wavelength of 700 nm
 51. Apparatus inaccordance with claim 45 wherein said second waveband comprises awaveband centered on a wavelength of 560 nm.
 52. Apparatus in accordancewith claim 45 wherein said third waveband comprises a waveband centeredon a wavelength of 473 nm.
 53. Apparatus in accordance with claim 45wherein one of said first, second or third wavebands comprises infra redlight.
 54. Apparatus in accordance with claim 45 wherein saidconcentration determination module comprises a look up table associatingpairs of first and second ratios generated by said ratio determinationmodule with items of data identifying concentrations of blood andmelanin which when illuminated with polarized light arc liable to remitcross polarized light having wavelengths falling within said first,second and third wavebands at said first and second ratios. 55.Apparatus in accordance with claim 54 wherein said pairs of first andsecond ratios and said concentrations of blood and melanin compriseratios and concentrations determined by analyzing samples of epithelialtissue.
 56. Apparatus in accordance with claim 54 wherein said pairs offirst and second ratios and said concentrations of blood and melanincomprise ratios and concentrations determined utilizing a mathematicalmodel of the expected remittance of illuminated light by samples ofepithelial tissue having differing concentrations of blood and melanin.57. Apparatus in accordance with claim 45 wherein said concentrationdetermination module is operable to determine values representative ofconcentrations of blood and melanin by applying a predeterminedmathematical function to first and second ratios for a position asdetermined by said ratio determination module.
 58. Apparatus inaccordance with claim 45 wherein said concentration determination modulecomprises a look up table associating pairs of first and second ratiosgenerated by said ratio determination module with items of dataidentifying concentrations of blood and tissue thickness which whenilluminated with polarized light arc liable to remit cross polarizedlight having wavelengths falling within said first, second and thirdwavebands at said first and second ratios.
 59. Apparatus in accordancewith claim 58 wherein said pairs of first and second ratios and saidconcentrations of blood and tissue thickness comprise ratios andconcentrations determined by analyzing samples of epithelial tissue. 60.Apparatus in accordance with claim 58 wherein said pairs of first andsecond ratios and said concentrations of blood and melanin compriseratios and concentrations determined utilizing a mathematical model ofthe expected remittance of illuminated light by samples of epithelialtissue having differing concentrations of blood and tissue thickness.61. Apparatus in accordance with claim 45 wherein said concentrationdetermination module is operable to determine values representative ofconcentrations of blood and tissue thickness by applying a predeterminedmathematical function to first and second ratios for a position asdetermined by said ratio determination module.
 62. Apparatus inaccordance with claim 45 wherein said polarized light source operable toilluminate a sample of epithelial tissue with polarized light comprises:a light source; and a polarizing filter arranged to polarize lightgenerated by said light source.
 63. Apparatus in accordance with claim62 wherein said light source is operable to illuminate a sample ofepithelial tissue sequentially with light having wavelengths fillingwithin different ones of said first, second, and third predeterminedwavebands.
 64. A method for determining the distribution of chromophoresand/or thickness of structural layers in a sample of epithelial tissue,the method comprising: illuminating a sample of epithelial tissue withpolarized light having wavelengths falling within a first, second, andthird predetermined wavebands; filtering light remitted from a sample ofepithelial tissue so as to filter out light polarized in the mannercorresponding to the polarized light utilized to illuminate the sampleof epithelial tissue; generating image data indicative of the intensityof filtered remitted light having wavelengths falling within said first,second and third predetermined wavebands; processing generated imagedata to determine or positions within images represented by said imagedata, a first ratio corresponding to the ratio of filtered remittedlight having wavelengths within said second waveband relative tofiltered remitted light having wavelengths within said first waveband,and a second ratio corresponding to the ratio of filtered remitted lighthaving wavelengths within said third waveband relative to filteredremitted light having wavelengths within said first waveband;determining for positions within an image represented by generated imagedata the concentrations of chromophores and/or thickness of structurallayers of said epithelial tissue at said positions in the sample ofepithelial tissue represented by said image data utilizing said firstand said second ratios determined for said positions; and outputtingdata representing said determined concentrations of chromophores and/orthickness of epithelial tissue for points in said sample of epithelialtissue.
 65. A method in accordance with claim 64 wherein said firstwaveband comprises a waveband corresponding to red light.
 66. A methodin accordance with claim 64 wherein said second waveband comprises awaveband corresponding to green light.
 67. A method in accordance withclaim 64 wherein said third waveband comprises a waveband correspondingto blue light.
 68. A method in accordance with claim 64 wherein one ofsaid first, second or third wavebands comprises infra red light.
 69. Amethod in accordance with claim 64 wherein said first waveband comprisesa waveband centered on a wavelength of 700 nm.
 70. A method inaccordance with claim 64 wherein said second waveband comprises awaveband centered on a wavelength of 560 nm.
 71. A method in accordancewith claim 64 wherein said third waveband comprises a waveband centeredon a wavelength of 473 nm.
 72. A method in accordance with claim 64wherein said determining for positions within an image represented bygenerated image data the concentrations of chromophores and/or thicknessof structural layers of said epithelial tissue comprises determining forpositions within an image represented by generated image data theconcentrations of blood and melanin in said epithelial tissue at saidpositions in the sample of epithelial tissue represented by said imagedata utilizing said first and said second ratios determined for saidpositions.
 73. A method in accordance with claim 64 wherein saiddetermining for positions within an image represented by generated imagedata the concentrations of chromophores and/or thickness of structurallayers of said epithelial tissue comprises determining for positionswithin an image represented by generated image data the concentrationsof blood in said epithelial and tissue thickness of said epithelialtissue at said positions in the sample of epithelial tissue representedby said image data utilizing said first and said second ratiosdetermined for said positions.
 74. A method in accordance with claim 64wherein said illuminating a sample of epithelial tissue with polarizedlight having wavelengths falling within a first, second, and thirdpredetermined wavebands comprises sequentially illuminating said sampleof epithelial tissue with polarized light having wavelengths fallingwithin different ones of said first, second and third predeterminedwavebands.